Renormalization approach to many-particle systems

Becker, K. W.; Hübsch, A.; Sommer, Torsten

doi:10.1103/physrevb.66.235115

Cited by 44 publications

(96 citation statements)

References 9 publications

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“…In this paper we have applied a recently developed renormalization approach [10] to the 'classical' problem of interacting electrons and phonons. By adding a small field to the Hamiltonian, which break the gauge symmetry, we directly derive a BCS-like gap equation for the coupled electron-phonon system.…”

Section: Discussionmentioning

confidence: 99%

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Renormalization of the electron-phonon interaction: a reformulation of the BCS-gap equation

Hübsch¹,

Becker

2003

The European Physical Journal B - Condensed Matter

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A recently developed renormalization approach is used to study the electron-phonon coupling in many-electron systems. By starting from an Hamiltonian which includes a small gauge symmetry breaking field, we directly derive a BCS-like equation for the energy gap from the renormalization approach. The effective electron-electron interaction for Cooper pairs does not contain any singularities. Furthermore, it is found that phonon-induced particle-hole excitations only contribute to the attractive electron-electron interaction if their energy difference is smaller than the phonon energy.

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Section: Discussionmentioning

confidence: 99%

“…The PRM [10] starts from the decomposition of a given many-particle Hamiltonian H into an unperturbed part H 0 and into a perturbation H 1 H = H 0 + εH 1 =: H(ε).…”

Section: Projector-based Renormalization Methods (Prm)mentioning

confidence: 99%

Renormalization of the electron-phonon interaction: a reformulation of the BCS-gap equation

Hübsch¹,

Becker

2003

The European Physical Journal B - Condensed Matter

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“…(1) have also been discussed in the framework of a renormalisation approach by Becker et al [18], which incorporates the use of hard cut-off functions. However, the authors use perturbation theory with respect to the hybridisation strength and neglect processes that connect different f sites, which is not sufficient to obtain the proper heavy fermion behaviour.…”

Section: A Periodic Anderson Modelmentioning

confidence: 99%

Flow equation approach to heavy fermion systems

Meyer

2004

Eur. Phys. J. B

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We use Wegner's flow equation method to investigate the infinite-U periodic Anderson model. We show that this method poses a new approach to the description of heavy fermion behaviour. Within this scheme we derive an effective Hamiltonian in which the c and f degrees of freedom are decoupled. By evaluating one-particle energies as well as correlation functions we find an electronic structure which comprises two gapped quasiparticle bands. We also address the lattice Kondo temperature, which shows a typical exponential dependence on the hybridisation energy. This energy scale exhibits a significant decrease compared to that of the single impurity Anderson model.

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“…To access the low-ω 0 regime and reconfirm the DMRG phase boundaries, obtained for the 1D Edwards model at larger values of ω 0 , we employ the analytical PRM approach. 25 The basic idea of the PRM is to construct-performing a sequence of discrete unitary transformations and eliminating all transitions with energy larger than a given cutoff energy-an effective non-interacting HamiltonianH with renormalized parameters (in the limit of vanishing cutoff energy). For the metallic state of the Edwards model, in momentum space, it takes the form been derived in Ref.…”

Section: A Ground-state Propertiesmentioning

confidence: 99%

Phase separation in the Edwards model

2012

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The nature of charge transport within a correlated background medium can be described by spinless fermions coupled to bosons in the model introduced by Edwards. Combining numerical density matrix renormalization group and analytical projector-based renormalization methods we explore the ground-state phase diagram of the Edwards model in one dimension. Below a critical boson frequency any long-range order disappears and the system becomes metallic. If the charge carriers are coupled to slow quantum bosons the Tomonaga-Luttinger liquid is attractive and finally makes room for a phase separated state, just as in the t-J model. The phase boundary separating the repulsive from the attractive Tomonaga-Luttinger liquid is determined from long-wavelength charge correlations, whereas fermion segregation is indicated by a vanishing inverse compressibility. On approaching phase separation the photoemission spectra develop strong anomalies. I. PROBLEMThe Edwards fermion-boson model 1,2 constitutes a paradigmatic model for the theoretical description of quantum transport in solids. Charge transport normally takes place in the presence of some background medium. 3Examples for such a "background" could be a spin-, charge-or orbital-ordered lattice, 4,5 but also a sequence of chemical side groups along the transport path, a deformable medium, or even a heat bath might be possible. In all these cases, the transfer of the charge carriers will be strongly influenced by fluctuations, which may exist in the background medium. The other way around, the properties of the background are quite often determined by the motion of the particle itself.Correlations inherent in such a complex interactive system are mimicked by a boson-affected hopping of spinless fermionic particles in the Edwards model. It reads:of energy ω 0 at the sites it leaves or enters. Such an excitation or de-excitation corresponds to a local "distortion" of the background. Because of quantum fluctuations the distortions are able to relax (∝ λ). The physically most interesting regimes in this setting are those of vanishing fermion density and of a half-filled band, representing doped Mott insulators, polaronic organics and charge-density-wave (CDW) systems 6-9 with possible relevance to high-T c superconductors, respectively. However, the Edwards model also reveals fascinating properties over the whole density range. On these grounds, the main goal of the present work is to pinpoint the ground-state phase diagram of the onedimensional (1D) Edwards model as a function of the band filling n. Thereby we demonstrate that this model indeed captures a number of very interesting phenomena, including e.g. electronic phase separation (PS). To obtain reliable information about the ground-state and spectral properties of the model in the thermodynamic limit, we employ numerical pseudosite density-matrix renormalization group (DMRG) and dynamical DMRG (DDMRG) techniques (supplemented by a careful finite-size scaling procedure, for details see Refs. 9, 21-24), in combination with ...

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Renormalization approach to many-particle systems

Cited by 44 publications

References 9 publications

Renormalization of the electron-phonon interaction: a reformulation of the BCS-gap equation

Renormalization of the electron-phonon interaction: a reformulation of the BCS-gap equation

Flow equation approach to heavy fermion systems

Phase separation in the Edwards model

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